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ArcCsch






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsch[z] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/01.29.26.0029.01









  


  










Input Form





ArcCsch[Sqrt[z]] - (Sqrt[z]/2) Sqrt[1/z] Log[4/z] + (Sqrt[z]/2) Sqrt[1/z] Sum[((-1)^k Pochhammer[1/2, k] z^k)/(k k!), {k, 1, n}] == (((-1)^n Sqrt[z])/(2 Sqrt[Pi])) Sqrt[1/z] MeijerG[{{1/2, 1, 1 + n}, {}}, {{1 + n}, {0, 0}}, z] /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{1, Infinity}], z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["ArcCsch", "[", SqrtBox["z_"], "]"]], "-", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["z_"], " ", SqrtBox[FractionBox["1", "z_"]], " ", RowBox[List["Log", "[", FractionBox["4", "z_"], "]"]]]], "+", RowBox[List[FractionBox["1", "2"], " ", SqrtBox["z_"], " ", SqrtBox[FractionBox["1", "z_"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k_", "=", "1"]], "n_"], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k_"], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k_"]], "]"]], " ", SuperscriptBox["z_", "k_"]]], RowBox[List["k_", " ", RowBox[List["k_", "!"]]]]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SqrtBox["z"]]], ")"]], " ", SqrtBox[FractionBox["1", "z"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "1", ",", RowBox[List["1", "+", "n"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "+", "n"]], "}"]], ",", RowBox[List["{", RowBox[List["0", ",", "0"]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["2", " ", SqrtBox["\[Pi]"]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]], "&&", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List["1", ",", "\[Infinity]"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2003-08-21





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